Efficiency of magnetic Penrose process in higher dimensional Myers-Perry black hole spacetimes
Abstract
In this paper, we consider a well-established magnetic Penrose process (MPP) and bring out its impact on the efficiency of energy extraction from higher dimensional (i.e., <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>D</a:mi><a:mo>></a:mo><a:mn>4</a:mn></a:mrow></a:math>) black holes. We derive the field equations of motion and determine the expressions for the energy efficiency of energy extraction for the case of higher dimensional black holes. We also examine the efficiency of energy extraction from black holes with (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>n</c:mi><c:mo>−</c:mo><c:mn>1</c:mn></c:mrow></c:math>) and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>n</e:mi></e:math> rotations. We demonstrate that black holes with (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mi>n</g:mi><g:mo>−</g:mo><g:mn>1</g:mn></g:mrow></g:math>) rotations has only one horizon, resulting in infinitely large energy efficiency even without MPP. On the other hand, for black holes with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>n</i:mi></i:math> rotations in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>D</k:mi><k:mo>></k:mo><k:mn>4</k:mn></k:math>, the energy efficiency is not infinitely large, but the efficiency can be significantly enhanced by MPP. This enhancement allows for arbitrarily large energy efficiency. We find that the efficiency of energy extraction can exceed 100% for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>D</m:mi><m:mo>=</m:mo><m:mn>5</m:mn></m:math>, 6 and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>D</o:mi><o:mo>=</o:mo><o:mn>7</o:mn></o:math>, 8 dimensions. Interestingly, for rotation parameters near the extremal value, the energy efficiency remains above 100% in <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>D</q:mi><q:mo>=</q:mo><q:mn>7</q:mn></q:math>, 8 compared to <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>D</s:mi><s:mo>=</s:mo><s:mn>5</s:mn></s:math>, 6. MPP can eventually make higher dimensional black holes more efficient even with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>n</u:mi></u:math> rotations. Published by the American Physical Society 2024